基于支持向量机的岩体力学参数反演及工程应用
|
摘要
基于支持向量机(SVM)的位移反分析是较新出现的一种岩土工程参数反演方法,它用训练得到的支持向量机模型代替数值模型实现岩体力学参数与位移间的复杂映射关系,大大提高了反演计算效率。与早期反分析中较多采用的神经网络方法相比,支持向量机在理论基础和求解算法方面都具有明显优势,日益受到岩土工程研究人员的重视。
本文围绕目前反分析方法存在的一些问题,首先从提高建模效率和模型计算精度的角度对地下工程数值建模方法进行探讨,然后从影响支持向量机泛化性能的主要因素,即支持向量机模型参数、支持向量机类型以及核函数形式三个方面对基于支持向量机的岩体力学参数反演方法展开系统研究,并应用于工程实践,主要内容概括如下:
(1)探讨了基于自然单元法的地下工程数值建模方法。为克服在处理地下工程无限域或半无限域问题时需要人为确定边界条件而带来计算误差的问题,引入无限元模拟无穷远处边界条件,与自然元相结合形成耦合分析方法,通过算例分析表明,耦合方法能够提高计算精度,降低对分析区域选取范围的要求,进而减少计算工作量;同时实现了基于自然元与无限元耦合方法的粘弹性分析,拓展了自然单元法在岩土工程中的适用范围。
(2)为克服传统参数选取方法存在的不足,研究了基于粒子群算法的支持向量机模型参数优化方法。为提高算法搜索能力,对标准粒子群算法适应值比较方式和粒子运动方式做出修改,使粒子移动更具有导向性和灵活性,同时为避免算法早熟采用同时考虑时间和粒子群聚集程度影响的动态自适应惯性权重,在此基础上提出一种改进粒子群算法;算例分析表明,与传统参数选择方法相比,采用该方法明显提高了参数搜索效率和相应支持向量机模型的预测精度。
(3)研究了基于最小二乘支持向量机(LS-SVM)的岩体力学参数反演方法。针对标准型支持向量机计算复杂度大的缺点,将最小二乘支持向量机代替标准型支持向量机,与改进粒子群算法相结合,用于围岩参数反演;同时为克服常规算法得到的最小二乘支持向量机的解丧失稀疏性的缺点,采用基于二次Renyi熵的增量迭代式回归算法训练最小二乘支持向量机模型;通过反演算例表明,将最小二乘支持向量机应用于岩体力学参数反演是可行的,与标准型支持向量机相比,采用最小二乘支持向量机能够有效提高反演计算效率。
(4)探讨了核函数形式对反演结果的影响。目前普遍采用的径向基核函数(RBF)由于缺乏平移正交性,使得相应支持向量机模型的逼近能力受到限制,间接影响参数辨识精度,为此引入小波和尺度函数作为LS-SVM的核函数用于岩体力学参数反演;并针对常规尺度函数局部性不足的缺点,根据相关理论构造出一种具有良好紧支性和光滑性的尺度核函数;算例分析表明,核函数的逼近性能对参数识别精度有较大影响,在满足容许精度要求的前提下,采用逼近能力强的核函数可以减少所需样本数量,从而降低计算量。
(5)以前面的工作为基础,结合王坑高速公路隧道项目,开展工程应用研究。在考虑爆破开挖影响的基础上,采用自然元与无限元耦合方法构建了模拟隧道施工过程的三维仿真模型;通过正交数值试验和影响度分析确定待反演参数,以实测变形为依据,用紧支尺度核最小二乘支持向量机反演岩体力学参数,通过对各测点实测变形序列与计算变形序列的灰色关联度分析检验了反演结果的合理性,最后利用反演参数对后续开挖断面的围岩变形实施预测并取得了较好的效果。
The displacement back analysis based on support vector machine (SVM) is a newly appeared parameters identification method of geotechnical engineering, which realizes the complex mapping relationship between mechanical parameters and deformations of rock mass using SVM model determined by a few learning examples instead of numerical model and improves inversion efficiency. Compared with artificial neural network (ANN), which is earlier used for back analysis, the SVM bears more excellent characteristics both in basic theory and solution method, so it has been paid increasingly more attention by researchers in geotechnical engineering.
In allusion to the disadvantages of present back analysis method, the numerical modeling method of underground engineering is discussed first in detailed, and then the method of rock mechanical parameter identification based on SVM is studied systematically from three aspects, parameters optimization of SVM, type of SVM, and the kernel function form, which are crucial factors affecting the generation ability of SVM, finally the research results was applied to real project. The major contents are as follows:
(1) The numerical modeling method of underground engineering based on natural element method (NEM) was discussed. Aimed at the defect that the errors was inevitably caused by selecting a certain finite region and setting the boundary conditions subjectively when treating infinite or half infinite domain problem in geotechnical engineering, the infinite element method(IEM) was introduced to simulate the boundary conditions at infinitely distant place, thus the coupling analysis method of NEM and IEM was provided. Through an example, the correctness of the computation method was proved. The results show that the coupling method improves the calculation precision and reduces the requirement for calculation range; meanwhile, visco-elastic analysis based on the coupling method is successfully implemented, which extends the application scope of NEM in geotechnical engineering.
(2) In order to overcome the shortcomings of conventional parameter selection methods, the parameter selection method based on particle swarm optimization (PSO) is addressed. By modifying the comparison mode of fitness value and the motion mode of individual particle of conventional PSO, and designing an auto-adaptive dynamic inertia weight which considers both the time and clustering degree of particles, an improved particle swarm optimization (IPSO) is proposed. Numerical results showed that, compared with traditional parameter selection methods, the new method obviously increases the parameter searching efficiency and the predictive precision of corresponding SVM.
(3) The surrounding rock parameters identification method based on least squares support vector machine (LS-SVM) is studied. By substituting LS-SVM for standard SVM, and combined with the improved particle swarm optimization (IPSO), a novel displacement back analysis method is provided. To ensure the sparsity of support vectors of LS-SVM, an iterative regression algorithm based on quadratic Renyi entropy and incremental learning algorithm is chosen to solve the LS-SVM model. Through examples of back analysis, the feasibility and effectiveness of applying LS-SVM to parameters inversion of rock mass is demonstrated, and the results show that, compared with standard SVM, inversion efficiency is greatly improved using LS-SVM.
(4) The influence of kernel function form on inversion results is discussed. Due to the lack of orthogonality by translation, the RBF kernel function, which is generally used for back analysis at present, restricts the generalization performance of corresponding SVM and impairs inversion precision indirectly. In view of this, the wavelet function and scaling function were used as kernel function for parameter inversion. In addition, aiming at the deficiency of locality of conventional scaling function, a new compact support scaling kernel function with good smoothness was constructed according to the related theory. The results of an inversion example showed that the approximation ability of kernel function has serious influence on parameter identification precision, and when the admissible accuracy is satisfied, less training examples is needed if using kernel function with better approximation ability, which means less computation cost.
(5) Based on above work, application study on back analysis was performed in Wangkeng expressway tunnel project. Using the coupling method of NEM and IEM, the 3D numerical model simulating tunnel construction was build, and the influence of excavation damage zone was considered. Through influence degree analysis, the parameters that would be identified were determined. Then the compact support scaling kernel LS-SVM was used for mechanical parameters inversion of surrounding rock. The space displacement sequence grey correction analysis indicated that the inversion results were credible. Finally, based on the identified parameters, the deformations of surrounding rock caused by subsequent excavation were successfully predicted.
本文围绕目前反分析方法存在的一些问题,首先从提高建模效率和模型计算精度的角度对地下工程数值建模方法进行探讨,然后从影响支持向量机泛化性能的主要因素,即支持向量机模型参数、支持向量机类型以及核函数形式三个方面对基于支持向量机的岩体力学参数反演方法展开系统研究,并应用于工程实践,主要内容概括如下:
(1)探讨了基于自然单元法的地下工程数值建模方法。为克服在处理地下工程无限域或半无限域问题时需要人为确定边界条件而带来计算误差的问题,引入无限元模拟无穷远处边界条件,与自然元相结合形成耦合分析方法,通过算例分析表明,耦合方法能够提高计算精度,降低对分析区域选取范围的要求,进而减少计算工作量;同时实现了基于自然元与无限元耦合方法的粘弹性分析,拓展了自然单元法在岩土工程中的适用范围。
(2)为克服传统参数选取方法存在的不足,研究了基于粒子群算法的支持向量机模型参数优化方法。为提高算法搜索能力,对标准粒子群算法适应值比较方式和粒子运动方式做出修改,使粒子移动更具有导向性和灵活性,同时为避免算法早熟采用同时考虑时间和粒子群聚集程度影响的动态自适应惯性权重,在此基础上提出一种改进粒子群算法;算例分析表明,与传统参数选择方法相比,采用该方法明显提高了参数搜索效率和相应支持向量机模型的预测精度。
(3)研究了基于最小二乘支持向量机(LS-SVM)的岩体力学参数反演方法。针对标准型支持向量机计算复杂度大的缺点,将最小二乘支持向量机代替标准型支持向量机,与改进粒子群算法相结合,用于围岩参数反演;同时为克服常规算法得到的最小二乘支持向量机的解丧失稀疏性的缺点,采用基于二次Renyi熵的增量迭代式回归算法训练最小二乘支持向量机模型;通过反演算例表明,将最小二乘支持向量机应用于岩体力学参数反演是可行的,与标准型支持向量机相比,采用最小二乘支持向量机能够有效提高反演计算效率。
(4)探讨了核函数形式对反演结果的影响。目前普遍采用的径向基核函数(RBF)由于缺乏平移正交性,使得相应支持向量机模型的逼近能力受到限制,间接影响参数辨识精度,为此引入小波和尺度函数作为LS-SVM的核函数用于岩体力学参数反演;并针对常规尺度函数局部性不足的缺点,根据相关理论构造出一种具有良好紧支性和光滑性的尺度核函数;算例分析表明,核函数的逼近性能对参数识别精度有较大影响,在满足容许精度要求的前提下,采用逼近能力强的核函数可以减少所需样本数量,从而降低计算量。
(5)以前面的工作为基础,结合王坑高速公路隧道项目,开展工程应用研究。在考虑爆破开挖影响的基础上,采用自然元与无限元耦合方法构建了模拟隧道施工过程的三维仿真模型;通过正交数值试验和影响度分析确定待反演参数,以实测变形为依据,用紧支尺度核最小二乘支持向量机反演岩体力学参数,通过对各测点实测变形序列与计算变形序列的灰色关联度分析检验了反演结果的合理性,最后利用反演参数对后续开挖断面的围岩变形实施预测并取得了较好的效果。
The displacement back analysis based on support vector machine (SVM) is a newly appeared parameters identification method of geotechnical engineering, which realizes the complex mapping relationship between mechanical parameters and deformations of rock mass using SVM model determined by a few learning examples instead of numerical model and improves inversion efficiency. Compared with artificial neural network (ANN), which is earlier used for back analysis, the SVM bears more excellent characteristics both in basic theory and solution method, so it has been paid increasingly more attention by researchers in geotechnical engineering.
In allusion to the disadvantages of present back analysis method, the numerical modeling method of underground engineering is discussed first in detailed, and then the method of rock mechanical parameter identification based on SVM is studied systematically from three aspects, parameters optimization of SVM, type of SVM, and the kernel function form, which are crucial factors affecting the generation ability of SVM, finally the research results was applied to real project. The major contents are as follows:
(1) The numerical modeling method of underground engineering based on natural element method (NEM) was discussed. Aimed at the defect that the errors was inevitably caused by selecting a certain finite region and setting the boundary conditions subjectively when treating infinite or half infinite domain problem in geotechnical engineering, the infinite element method(IEM) was introduced to simulate the boundary conditions at infinitely distant place, thus the coupling analysis method of NEM and IEM was provided. Through an example, the correctness of the computation method was proved. The results show that the coupling method improves the calculation precision and reduces the requirement for calculation range; meanwhile, visco-elastic analysis based on the coupling method is successfully implemented, which extends the application scope of NEM in geotechnical engineering.
(2) In order to overcome the shortcomings of conventional parameter selection methods, the parameter selection method based on particle swarm optimization (PSO) is addressed. By modifying the comparison mode of fitness value and the motion mode of individual particle of conventional PSO, and designing an auto-adaptive dynamic inertia weight which considers both the time and clustering degree of particles, an improved particle swarm optimization (IPSO) is proposed. Numerical results showed that, compared with traditional parameter selection methods, the new method obviously increases the parameter searching efficiency and the predictive precision of corresponding SVM.
(3) The surrounding rock parameters identification method based on least squares support vector machine (LS-SVM) is studied. By substituting LS-SVM for standard SVM, and combined with the improved particle swarm optimization (IPSO), a novel displacement back analysis method is provided. To ensure the sparsity of support vectors of LS-SVM, an iterative regression algorithm based on quadratic Renyi entropy and incremental learning algorithm is chosen to solve the LS-SVM model. Through examples of back analysis, the feasibility and effectiveness of applying LS-SVM to parameters inversion of rock mass is demonstrated, and the results show that, compared with standard SVM, inversion efficiency is greatly improved using LS-SVM.
(4) The influence of kernel function form on inversion results is discussed. Due to the lack of orthogonality by translation, the RBF kernel function, which is generally used for back analysis at present, restricts the generalization performance of corresponding SVM and impairs inversion precision indirectly. In view of this, the wavelet function and scaling function were used as kernel function for parameter inversion. In addition, aiming at the deficiency of locality of conventional scaling function, a new compact support scaling kernel function with good smoothness was constructed according to the related theory. The results of an inversion example showed that the approximation ability of kernel function has serious influence on parameter identification precision, and when the admissible accuracy is satisfied, less training examples is needed if using kernel function with better approximation ability, which means less computation cost.
(5) Based on above work, application study on back analysis was performed in Wangkeng expressway tunnel project. Using the coupling method of NEM and IEM, the 3D numerical model simulating tunnel construction was build, and the influence of excavation damage zone was considered. Through influence degree analysis, the parameters that would be identified were determined. Then the compact support scaling kernel LS-SVM was used for mechanical parameters inversion of surrounding rock. The space displacement sequence grey correction analysis indicated that the inversion results were credible. Finally, based on the identified parameters, the deformations of surrounding rock caused by subsequent excavation were successfully predicted.
引文
[1]Kavanagh K T,Clough R W.Finite element application in the characterization of elastic solid[J].Int J Solid Structures,1972,(7):11-23.
[2]Kirsten H A D.Determination of rock mass elastic moduli by back analysis of deformation measurement[A].In:Proc Stmp on Expliration for Rock Eng[C].Johannesburg,1976,1154-1160.
[3]Maiar G,Jurina L,Podolak K.On model identification problem in rock mechanics [A].In:Proceedings symposium on the Geotechnics of Structurally Complex Formations[C].Capri,1977:257-261.
[4]Kovari K.Integrated Measuring Technique for Rock Pressure Determination[C].Int.Symp.On Measurement in Rock Mech.,Zurich,April,1977.
[5]Gioda G,Maier G.Direct search solution of an inverse problem in elasto-plasticity,indentification of cohesion,fricition angle and in-situ stress by pressure tunnel tests[J].Int.J.Num Methods in Eng,1980(15):1823-1834.
[6]Sakurai S,Takeuchi K.Back Analysis of measured displacement of tunnel[J].Rock Mech And Rock Eng,1983,16(3):173-180.
[7]杨林德.岩土工程问题的反演理论与工程实践[M].北京:科学出版社,1995:23-29.
[8]杨志法,王思敬,冯紫良,等.岩土工程反分析原理及应用[M].北京:地震出版社,2002:1-3.
[9]Pierpaolo Oreste.Back-analysis techniques for the improvement of the understanding of rock in underground constructions[J].Tunnelling and Underground Space Technology,2005(20):7-21.
[10]Sakurai S.Determination of initial stresses and mechanical Properties of viscoelastic underground medium[C].Proc.3~(rd) ISRM Cong.,Denver,1974,Π-B,1169-1174.
[11]刘允芳.弹性介质岩体中非圆形洞室位移反分析计算[J].岩石力学与工程学报,1986,5(5):141-144.
[12]薛琳,杨志法.粘弹性岩体力学参数的解析法[R].中科院地质研究所工程地质力学开放实验室1992年报.北京:地震出版社,1992:71-84.
[13]薛琳,杨志法.隧道周围粘弹性岩土介质蠕变柔量反演[R].中科院地质研究所工程地质力学开放实验室1992年报.北京:地震出版社,1992:178-190.
[14]Gioda G,Jurina L.Numerical identification of soil-structure interaction Pressures.Int.J.for Num.Anal.& Method in Geomech.,1981,(5):33-56.
[15]Wang Zhiyin,Liu Huaiheng.Back analysis of measured rheologic displacements of underground opening[C].In:Proe.6~(th) Conf.on Num.Meth.in Geomechanics,Austria,1988:2291-2297.
[16]杨林德.确定矿山巷道初始地应力方法的研究[J].同济大学学报,1986,14(2):161-166.
[17]杨志发,刘竹华.位移反分析在地下工程设计中的初步应用[J].地下工程,1981(2):20-24.
[18]杨志法,丁恩保,张三旗.地下工程平面问题弹性有限元图谱[M].北京:科学出版社,1989.
[19]吕爱钟,蒋斌松.岩石力学反问题[M].北京:煤炭工业出版社,1998.
[20]蒋斌松.巷道支架荷载反算方法[C].第四届全国岩土力学数值分析与解析方法讨论会论文集.武汉:武汉测绘科技大学出版社,1991,139-147.
[21]朱珍德,胡定.隧洞围岩压力位移反分析原理和方法[J].地下空间,1999,19(3):169-173.
[22]吕爱钟,蒋斌松.岩石力学反问题的几个基本问题[J].岩石力学与工程学报,2002,21(增刊):1921-1926.
[23]张中生,陈子萌,蒋斌松.地下结构荷载反算中解的稳定性研究[J].中国矿业,1999,8(5):79-84.
[24]张中生,陈子萌,朱维申.地下结构荷载的广义反演方法[J].土木工程学报,2001,34(2):38-42.
[25]张中生.地下结构荷载反算中的测线网优化布置[J].岩石力学与工程学报,2000,19(2):219-224.
[26]Gioda G.,etc.Back analysis procedures for the interpretation of field measurements in geomechanics[J].Int.J.for Num.& Anal.Methods in Geom.,1987(10):521-552.
[27]冯紫良,杨林德,李成江.初始地应力的反推原理[J].隧道工程,1985(4):44-50.
[28]冯紫良,杨林德.初始地应力的反推原理[J].同济大学学报,1983(3):18-25.
[29]杨林德,等.初始地应力位移反分析的有限单元法[J].同济大学学报,1985,(4):15-20.
[30]王芝银,刘怀恒.粘弹塑性有限元分析及其在岩石力学与工程中的应用[J].西安矿业学院学报,1985,5(1):86-101.
[31]陶振宇,曾庆义.地应力场的函数反分析[J].武汉水利电力学院学报,1987(3):21-27.
[32]庞作会,陈文胜,等.复杂初始地应力场的反分析[J].岩土工程学报,1998, 20(4):362-367.
[33]李守巨,张军,刘迎曦,等.基于优化算法的岩体初始应力场随机识别方法[J].岩石力学与工程学报,2004,23(23):4012-4016.
[34]易达,陈胜宏,葛修润.岩体初始应力场的遗传算法与有限元联合反演法[J]。岩土力学,2004,25(7):1077-1080.
[35]Arai R.An inverse problem approach to the prediction of Multi-dimensional consolidation behavior[J].Solids and Foundations,1984,24(1):95-108.
[36]朱志伟,冯紫良,刘学山.深基坑工程土层参数反演及挡墙内力预报[J].岩土力学,1999,20(4):63-68.
[37]刘学增,朱合华.考虑动态施工过程的岩土介质横观各向同性粘弹性反分析及其工程应用[J].岩土力学与工程学报,2002(1):89-92.
[38]刘迎曦,王登刚,李守巨,等.识别混凝土重力坝弹性模量的一种新方法[J].大连理工大学学报,2000,40(2):144-147.
[39]王复明,魏翠玲,周晶.路面结构的动态反分析[J].工程力学,2002,19(1):121-124,93.
[40]李宁,段小强,陈方方,等.围岩松动圈的弹塑性位移反分析方法探索[J].岩石力学与工程学报,2006,25(7):1304-1308.
[41]刘保国,郭忠平.岩体粘塑性流动系数γ的反演计算[J].岩土工程学报,1999,21(2):213-216.
[42]Gioda G,Sakurai S.Back analysis procedures for the interpretation of field measurements in geomechanics[J].Int.J.for Num.& Anal.Meth.in Geomech.,1987,11:555-583.
[43]袁勇,孙钧.岩体本构模型反演识别理论及其工程应用[J].岩石力学与工程学报,1993,12(3):232-39.
[44]袁勇,孙钧.岩土工程的系统辨识理论及工程应用[D].上海:同济大学,1991.
[45]高玮,郑颖人.基于遗传算法的岩土本构模型辨识[J].岩石力学与工程学报,2002,21(1):8-11.
[46]高玮,郑颖人.采用快速遗传算法进行岩土工程反分析[J].岩土工程学报,2001,23(1):120-122.
[47]高玮,郑颖人,冯夏庭.岩土本构模型识别的仿生算法研究[J].岩土力学,2004,25(1):31-36.
[48]高玮,郑颖人.基于生态竞争模型的岩土本构模型辨识新算法[J].岩土工程学报,24(1):93-97.
[49]高玮,冯夏庭.岩体本构模型智能识别的若干研究[J].岩石力学与工程学报, 2002,21(增2):2532-2538.
[50]刘保国,孙钧.岩体流变本构模型的辨识及其应用[J].北方交通大学学报,1998,22(4):10-14.
[51]孙钧.岩土材料流变及其工程应用[M].北京:中国建筑工业出版社,1999.
[52]朱珍德,徐卫亚.岩体粘弹性本构模型辨识及其工程应用[J].岩石力学与工程学报,2002,21(11):1605-1609.
[53]徐日庆,龚晓南,王明洋,等.枯弹性本构模型的识别与变形预报[J].水利学报,1998,(4):82-86.
[54]刘保国,孙钧.岩体粘弹性模型本构模型辨识的一种方法[J].工程力学,1999,16(1):12-17.
[55]刘世君,徐卫亚,邵建富.岩石粘弹性模型辨识及参数反演[J].水利学报,2002,(6):101-106.
[56]孙钧,蒋树屏,袁勇,等编著.岩石力学反演问题的随机理论与方法[M].汕头:汕头大学出版社,1996.
[57]黄宏伟,孙钧.基于Bayesian广义参数反分析[J].岩石力学与工程学报,1994,13(3):219-228.
[58]袁勇,孙钧.岩土工程优化反演的目标函数[J].岩石力学与工程学报,1994,13(2):29-37.
[59]朱永全,景诗庭,张清.围岩参数Monte-Carlo有限元反分析[J].岩土力学,1995,16(3):29-34.
[60]林育梁,樱井春铺.应用模糊有限元法的一种反分析形式[J].岩土工程学报,1995,17(5):48-52.
[61]蒋树屏.扩张卡尔曼滤波器有限元耦合算法及其隧道工程应用[J].土工程学报,1996,18(4):11-19.
[62]杨成祥,冯夏庭,陈炳瑞.基于扩展卡尔曼滤波的岩石流变模型参数辨识[J].岩石力学与工程学报,2007,26(4):754-761.
[63]陈斌.岩土工程随机反演分析及工程应用[D].河海大学博士论文,2001.
[64]陈斌,刘宁,周家守,等.岩土工程反分析的最大熵原理[J].河海大学学报(自然科学版),2002,30(6):52-55.
[65]Gioda G,Pnadolfi A,Cividini A.A comparative evaluation of some back analysis algorithms and their application to in-situ load tests[C].In:Proc.2~(nd) Int.Symp.on Field Measurement in Geom.,1987,1134-1144.
[66]吕爱钟.地下巷道弹性位移反分析各种优化方法的探讨[J].岩土力学,1996,17(2):29-34.
[67]孙钧,黄伟.岩石力学参数弹塑性反演问题的优化方法[J].岩石力学与工程学报,1992,11(3):221-229.
[68]席裕庚,柴天佑,恽为民.遗传算法综述[J].控制理论与应用,1996,13(6):697-708.
[69]陈建安,郭大伟,徐乃平,等.遗传算法理论研究综述[J].西安电子科技大学学报,1998,25(3):363-368.
[70]王登刚,刘迎曦,李守巨.岩土工程位移反分析的遗传算法[J].岩石力学与工程学报,2000,19(增刊):979-982.
[71]李守巨.基于计算智能的岩土力学模型参数反演方法及其工程应用[D].大连理工大学博士学位论文,2004.
[72]丁德馨,张志军,孙钧.弹塑性位移反分析的遗传算法研究[J].工程力学,2003,20(6):1-5.
[73]Colorni A,Dorigo M,Maniezzo V.Distributed Optimization by ant colonies[C].In:Varela F,Bougrine Ped.Proc 1st European Conefrence on Artifieial Life.France:Elsevier,1991,131-142.
[74]Dorigo M,Mnaiezzo V,Colorni A.The ant system:optimization by a colony of cooperating agents[J].IEEE Trans Syst Man Cybern-Part B,1996,26(1):29-41.
[75]Conre D,Dorigo M,Glover F.New ideas in optimization[M].London:Mc Grwa-Hill,1999.
[76]田明俊.智能反演算法及其应用研究[D].大连理工大学博士学位论文,2006.
[77]田明俊,周晶.基于蚁群算法的土石坝土体参数反演[J].岩石力学与工程学报,2005,24(8):1411-1416.
[78]Kennedy J,Eberhart R C.Particle swarm optimization[A].Proceedings of IEEE International Conference on Neural Network[C].New York:1995,1942-1948.
[79]Eberhart R C,Yuhui Shi.Particle swarm optimization:development,application and resources[A].Procedings of Evolutionary Computation[C].New York:IEEE Press.2001,81-86.
[80]高玮.基于粒子群优化的岩土工程反分析研究[J].岩土力学,2006,27(5):795-798.
[81]苏国韶,冯夏庭.基于粒子群算法的高地应力条件下硬岩本构模型的参数辨识[J].岩石力学与工程学报,2006,24(17):3030-3034.
[82]高玮,冯夏庭.基于免疫连续蚁群算法的岩土工程反分析研究[J].岩土力学与工程学报,2005,24(23):4266-4271.
[83]田明俊,周晶.岩土工程参数反演的一种新方法[J].岩石力学与工程学报, 2005,24(9):1492-1496.
[84]李守巨,刘迎曦,陈昌林,等.基于混合遗传算法的混凝土大坝力学参数反演[J].大连理工大学学报,2004,44(2):195-199.
[85]乐金朝,刘凤娥,王复明.路面结构模量反算的遗传—模拟退火算法[J].计算力学学报,2004,21(1):88-92.
[86]刘福深,刘耀儒,杨强,等.基于改进遗传算法的拱坝位移反分析[J].岩石力学与工程学报,2005,24(23):4341-4345.
[87]Feng Xia-Ting,Chen Bing-Rui,Yang Chengxiang,et al.Identification of visco-elastic models for rocks using genetic programming coupled with the modified particle swarm optimization algorithm[J].International Journal of Rock Mechanics and Mining Sciences,2006,43(5):789-801.
[88]Xia-ting Feng,Katsuyama K,Yong-jia Wang,et al.A new direction-intelligent rock mechanics and rock engineering[J].Int.J.rock Mechanics and Mining Science,1997.
[89]Feng Xia-Ting,Zhao Hongbo,Li Shaojun.A new displacement back analysis to identify mechanical geo-material parameters based on hybrid intelligent methodology [J].International Journal for Numerical and Analytical Methods in Geomechanics,2004,28(11):1141-1165.
[90]Shihui Li,Jie Yang,Weidong Hao,Yanjun Shang.Intelligent back-analysis of displacements monitored in tunneling[J].International Journal of Rock Mechanics &Mining Sciences,2006,(43):1118-1127.
[91]冯夏庭,张治强,杨成祥,等.位移反分析的进化神经网络方法研究[J].岩石力学与工程学报,1999,18(5):497-502.
[92]冯夏庭.智能岩石力学导论[M].北京:科学出版社,2000.
[93]张志军,丁德馨.位移反分析的人工神经网络方法研究[J].南华大学学报(自然科学版),2005,19(2):1-5.
[94]江权,冯夏庭,苏国韶,等.基于松动圈-位移增量监测信息的高地应力下洞室群岩体力学参数的智能反分析[J].岩石力学与工程学报,2007,26(增1):2654-2612.
[95]梁桂兰,徐卫亚,韦杰,等.位移反分析的APSO-WNN模型研究及应用[J].岩石力学与工程学报,2007,26(6):1251-1257.
[96]冯建龙,张孟喜.BP网络在双连拱隧道围岩参数反分析中的应用[J].上海大学学报(自然科学版),2005,11(3):293-298.
[97]易小明,陈卫忠,李术才,等.BP神经网络在分岔隧道位移反分析中的应用[J]. 岩石力学与工程学报,2006,25(增2):3927-3932.
[98]VAPNIK V.Statistical Learning Theory[M].New York:Wiley,1998.
[99]赵洪波.非线性岩土力学行为的支持向量机研究[M].中科院武汉岩土力学研究所,博士学位论文,2003.
[100]赵洪波,冯夏庭.位移反分析的进化支持向量机研究[J].岩石力学与工程学报,2003,22(10):1618-1622.
[101]许传华,任青文,周庆华.基于支持向量机和模拟退火算法的位移反分析[J].岩石力学与工程学报,2005,24(22):4134-4138.
[102]许传华,任青文,郑治,等.索风营水电站洞室岩体力学参数的位移反分析[J].岩土工程学报,2006,28(11):1981-1985.
[103]姜谙男.基于三维数值模拟-SVM非线性模型的大型洞室群围岩参数进化识别[J].水力发电学报,2006,25(5):97-101.
[104]刘开云,乔春生,刘保国.基于改进GA-SVR算法的隧道工程三维弹塑性模型参数的智能辨识[J].岩石力学与工程学报,2007,26(6):1164-1172.
[105]余志雄,周创兵,陈益锋,等.基于v-SVR和GA的初始地应力场位移反分析方法研究[J].岩土力学,2007,28(1):152-158.
[106]赵洪波.基于微粒群优化的智能位移反分析研究[J].岩土工程学报,2006,28(11):2035-2038.
[107]K.J.Bathe and E.L.Wilson.Numerical Method in Finite Element Analysis[M],1976.
[108]Belytschko T,Lu Y Y,Gu L.Element-free Galerkin method[J].Int.J.Num.Meth.Eng,1994,37(2):229-256.
[109]宋康祖,陆明万,张雄.固体力学中的无网格方法[J].力学进展,2000,30(3):55-56.
[110]Braun J,Sambridge M.A numerical method for solving partial differential equations on highly irregular evolving grids[J].Nature,1995,376:655-660.
[111]蔡永昌,朱合华.岩土工程数值计算中的无网格法及其全自动布点技术[J].岩土力学,2003,24(1):21-24.
[112]蔡永昌,朱合华,夏才初.无网格自然邻接点法及其在岩土工程数值模拟中的应用[J1.岩石力学与工程学报,2005,24(11):1888-1924.
[113]朱合华,杨宝红,蔡永昌,徐斌.无网格自然单元法在弹塑性分析中的应用[J].岩土力学,2004,25(4):671-674.
[114]张英新,王建华,高绍武.二维弹塑性自然单元法算法实现[J].上海交通大学学报,2005,39(5):727-730.
[115]Sukumar N,Moran,Belytschko T.The nature element method in solid mechanics[J].Int J Num Meth Eng,1998,43:839-887.
[116]N.Sukumar,B.Moran,A.Yu Semenov,et al.Natural neighbor Galerkin method[J].Int.J.Numer.Meth.Engng.,2001,50:1-27.
[117]Belikov V V,Semenov A Y.Non-Sibson interpolation on arbitrary system of points in Euclidean space and adaptive isolines generation[J].Applied Numerical Mathematics,2000,32:371-387.
[118]卢波,葛修润,王水林.自然单元法数值积分方案研究[J].岩石力学与工程学报,2005,24(1):1917-1924.
[119]Jeong Wahn Yoo,Brian Moran,Jiun-Shyan Chen.Stabilized conforming nodal integration in the natural-element method[J].Int.J.Numer.Meth.Engng.,2004,60:861-890.
[120]Bettess P,Zienkiewicz O C.Diffraction and refraction of surface waves using finite and infinite elements[J].International Journal for Numerical Methods in Engineering,1977,11:1271-1290.
[121]Astley R J,Eversman W.Wave envelope and infinite element schemes for fan noise radiation from turbofan inlets[C].AIAA-83-0709,1983.
[122]Astley R J,Macaulay G J.Mapped wave envelope elements for acoustical radiation and scattering[J].Journal of Sound and Vibration,1994,170(1):97-118.
[123]杨瑞梁,汪鸿振.一种新的声无限元法[J].振动与冲击,2003,22(3):21-24.
[124]赵崇斌,张楚汉,张光斗.用无穷元模拟半无限平面弹性地基[J].清华大学学报,1986,26(1):51-64.
[125]燕柳斌.用三维映射无限元模拟重力坝地基[J].水利学报,1991,10:7-12.
[126]周世良,胡晓,王江.无限元在岩土工程数值分析中的应用[J].重庆交通学院学报,2004,23(增刊):61-64.
[127]卢波.自然单元法的发展及其应用[D].中国科学院:武汉岩土力学所,博士学位论文,2005.
[128]张雄,刘岩.无网格法[M].北京:清华大学出版社,2004.
[129]孙钧.岩土材料流变及其工程应用[M].北京:中国建筑工业出版社,1999.
[130]孙钧,汪炳鉴.地下工程有限元解析[M].上海:同济大学出版社,1988.
[131]D.R.J.Owen,E.Hinton.Finite Element In Plasticity-Theory And Practice[M].Pinerige Press Limited,1980.
[132]李军强,刘宏昭,王忠民.线性粘弹性本构方程及其动力学应用研究综述[J].振动与冲击,2005,24(2):116-121.
[133]杨挺青.粘弹性力学[M].武汉:华中理工大学出版社,1990.
[134]Vapnik V.The nature of statistical learning theory[M].New York:Springer-Verlag,1999.
[135]张学工,译.统计学习理论的本质[M].北京:清华大学出版社,2000.
[136](英)克里斯特安尼(Cristianini,N.)等著:李国正,王猛,曾华军,译.支持向量机导论[M].北京:电子工业出版社,2004.
[137]邓乃扬,田英杰.数据挖掘中的新方法-支持向量机.北京:科学出版社,2004.
[138]张学工.关于统计学习理论与支持向量机[J].自动化学报,2000,26(1):37-42
[139]Cortes C.,Vapnik V.Support Vector Networks[J].Machine Learning,1995,Vol.20:273-297.
[140]Osuna E.,Freund R.An Improved Training Algorithm for Support Veetor Machines[C].In:Proceedings of the IEEE Workshop on Neural Networks for Signal Processing,1997.
[141]Platt J.C.Sequential Minimal Optimization:A Fast Algorithm for Training Support Vector Machines[R].Technical Report MSR-TR-98-14,Aprail,21,1998.
[142]Alex J Smola,Bernhard Schoelkopf.A tutorial on support vector regression[R].NeuroCOLT2 Technical Report Series NC2-TR-1998030,1998.
[143]Smola A,Murata N,Scholkopf B,Muller K.Asymptotically optimal choice of ε-loss for support vector machines[C].Proceedings of ICANN 1998.
[144]Kwok J T.Linear dependency between ε and the input noise in ε-support vector regression[A].In G.Dorffiner,H.Bishof,and K.Hornik(Eds.),ICANN2001,405-410.
[145]Mattera D,Haykin S.Support vector machines for dynamic reconstruction of a chaotic system[A].In B.Scholkopf,J.Burges,and A.Smola(Eds.),Advances in kernel methods:Support vector machine[M].Cambridge,MA:MIT Press,1999.
[146]Cherkassky V,Yunqian Ma.Practical Selection of SVM Parameters and Noise Estimation for SVM Regression[J].Neural Networks,2004,17:113-126.
[147]B.Baesens,S.Viaene,T.Van Gestel,J.A.K.Suykens,G..Dedene,B.De Moor,J.Vanthienen.An empirical assessment of kernel type performance for least squares support vector machine classification[C].Proceedings of Forth International on Knowledge-based Intelligent Engineer system and Allied Technologies.Brighton,UK 2000:313-316.
[148]K.Ito,R.Nakano.Optimizing Support Vector regression hyperparameters based on cross-validation[C].Proceedings of the International Joint Conference on Neural Networks.2003,3:2077-2082.
[149]Gavin C.,Cawley,Nicola L.C.,Talbot.Fast exact leave-one-out cross-validation of sparse least-squares support vector machines[J].Neural Networks.2004,17(10):1467-1475.
[150]郭辉,刘贺平,王玲.最小二乘支持向量机参数选择方法及其应用研究[J].系统仿真学报,2006,18(7):2033-2036,2051.
[151]Chapelle O.,Vapnic V.Choosing multiple parameters for support vector machines[J].Machine Learning,2002,(46):131-159.
[152]CHEN Pengwei,WANG Jungying,LEE Hahnming.Model selection of SVMs using GA approach[C].//Proc of 2004 IEEE Int Joint Conf on Neural Networks.Piscataway,NJ:IEEE Press,2004:2035-2040.
[153]ZHENG Chunhong,JIAO Licheng.Automatic parameters selection for SVM based on GA[C].//Proc of the 5th World Congress on Intelligent Control and Automation.Piscataway,NJ:IEEE Press,2004:1869-1872.
[154]杜京义,候媛彬.基于遗传算法的支持向量回归机参数选取[J].系统工程与电子技术,2006,28(9):1430-1433.
[155]陈果.基于遗传算法的支持向量机分类器模型参数优化[J].机械科学与技术,2007,26(3):347-350.
[156]邵信光,杨慧中,陈刚.基于粒子群算法的支持向量机参数选择及其应用[J].控制理论与应用,2006,23(5):740-744.
[157]李爱国.多粒子群协同优化算法[J].复旦学报(自然科学版),2004,43(5):923-925.
[158]吕振肃,侯志荣.自适应变异的粒子群优化算法[J].电子学报,2004,3:417-421
[159]Angeline P.Using selection to improve Particle swarm optimization[C].IEEE International Conference on Evolutionary Computation,Anchorage,Alaska,1998:84-89.
[160]Shi Y,Eberhart R.A modified Particle swarm optimizer[C].IEEE World Congress on Computational Intelligence,1998:69-73.
[161]刘建华,樊晓平,瞿志华.一种惯性权重动态调整的新型粒子群算法[J].计算机工程与应用,2007,43(7):68-70.
[162]郭文忠,陈国龙.粒子群优化算法中惯性权值调整的一种新策略[J].计算机工程与科学,2007,29(1):70-72,75.
[163]Clerc M.The swarm and the queen:towards a deterministic and adaptive particle swarm optimization[C].Proceedings of the 1999 Congress on Evolutionary computation,1999,.3:1951-1957.
[164]Kennedy J.Small worlds and mega-minds:effects of neighbourhood topology on particle swarm performance[C].Proceedings of IEEE Congress on Evolutionary Computation.1999,Vol.3:1931-1938.
[165]Higashi N,Iba H.Particle swarm optimization with Gaussian Mutation[C].//Proceedings of the 2003 Congress on Evolutionary Computation.Piscataway,NJ:IEEE Press,2003:72-89.
[166]高鹰,谢胜利.免疫粒子群优化算法[J].计算机工程与应用,2004,40(6):4-6.
[167]Brskar S,Suganthan P N.A Novel Concurrent Particle Swarm Optimization[C].//Proceedings of the 2004 Congress on Evolutionary Computation.Piscataway,NJ:IEEE Press,2004,792-796.
[168]Ven den Bergh F,Engelbrecht A.P..Using neighbourhoods with the guaranteed convergence PSO[C].Proceedings of the 2003 IEEE,Swarm Intelligence Symposium,2003:235-242.
[169]谭皓,沈春林,李锦.混合粒子群算法在高维复杂函数寻优中的应用[J].系统工程与电子技术,2005,27(8):1471-1474.
[170]陈贵敏,贾建援,韩琪.粒子群优化算法的惯性权值递减策略研究[J].西安交通大学学报,2006,(1):
[171]高鹰,谢胜利.基于模拟退火的粒子群优化算法[J].计算机工程与应用,2004,24(1):47-50.
[172]袁亚湘,孙文瑜,著.最优化理论与方法[M].北京:科学出版社,1997.
[173]G.Cauwenberghs,T.Poggio.Incremental and decremental support vector machine learning[C],in Advances in Neural Information Processing Systems,Cambridge,MA:MIT Press,2001,13:426-433.
[174]F.Perez-Cruz,A.Navia-Vazquez,R L.Alarcon-Diana,and A.Artes-Rodriguez.An IRWLS procedure for SVR[C].In Proc.of the EUSIPCO,Finland,Sept 2000.
[175]Suykens J A K,Vandewalle J.Least squares Support Vector Machines Classifiers[J].Neural Processing Letters,1999,9(3):293-300.
[176]J.A.K.Suykens,L.Lukas,et al.Sparse approximation using least squares support vector machines[C].In Proc.Of the IEEE International Symposium on Circuits and Systems(ISCAS 2000),Geneva,Switzerland,(2000):757-760.
[177]B J de Kruif,T J de Vries.Pruning error minimization in least squares support vector machines[J].IEEE Trans on Neural Networks,2003,14(3):696-702.
[178]X Y Zeng,X W Chen.SMO-based pruning methods for sparse least squares support vector machines[J].IEEE Trans on Neural Networks,2005,16(6):1541-1546.
[179]杨晓伟,路节,张广全.一种高效的最小二乘支持向量机分类器枝剪算法[J].计算机研究与发展,2007,44(7):1128-1136.
[180]甘志良,孙宗海,孙优贤.稀疏最小二乘支持向量机[J].浙江大学学报,2007,41(2):245-248.
[181]陶少辉,陈德钊,胡望明.最小二乘支持向量机分类器的高稀疏化及应用[J].系统工程与电子技术,2007,29(8):1351-1355.
[182]M.Espinoza,J.A.K.Suykens,B.D.Moor.Load forecasting using fixed-size least squares support vector machines[C].8th International Workshop on Artificial Neural Networks,IWANN 2005,Lecture Notes in Computer Science,2005,3512:1018-1026.
[183]M.Espinoza,J.A.K.Suykens,B.D.Moor.Fixed-size least squares support vector machines:a large scale application in electrical load forecasting[J].Computational Management Science,2006,(3):113-129.
[184]吴春国.广义染色体遗传算法与迭代式最小二乘支持向量机回归算法研究[D].吉林大学博士学位论文,2006.
[185]姜静清.最小二乘支持向量机算法及应用研究[D].吉林大学博士学位论文,2007.
[186]K.I.Diamantaras,S.Y.Kung.Principal Component Neural Networks:Theory and Applications[M].New York:John Wiley and Sons,1996.
[187]J.H.Liu,J.E Chen,et al.Online LS-SVM for function estimation and classification[J].Journal of University of Science and Technology,Beijing,2003,10(5):73-77.
[188]S.Vingaa,S.Jonas,J.A.Almeida.Renyi continuous entropy of DNA sequences [J].Journal of Theoretical Biology,2004,231:377-388.
[189]C.E.Shannon.A mathematical theory of communication[J].Bell Syst.Tech.J.1948,27:379-423,623-656.
[190]A.Renyi.On measures of entropy and information[C].Proceedings of the Fourth Berkeley Symposium on Mathematics,Statistics and Probability,University of California Press,Berkeley,CA,1961,1:547-561.
[191]A.Renyi.Introduction a la theorie de linformation.Calcul des probabilites[M]. Dunod,Paris,1966.
[192]M.Girolami.Orthogonal series density estimation and the kernel eigenvalue problem[J].Neural Computation,2002,14(3):669-688.
[193]刘贵忠,邸双亮.小波分析及其应用[M].西安:西安电子科技大学出版社,1992.
[194]Zhang Q H,Benveniste A.Wavelet network[J].IEEE Trans on Neural Network,1992,3(6):889-898.
[195]Zhang Q.Using Wavelet Networks in Nonparametric Estimation[J].IEEE Tmas.Neural Networks,1997,8(2):227-236.
[196]Zhang J,Walter G G.,Lee W N W.Wavelet Neural Networks for Function Learning[J].IEEE Trs.Signal Processing,1995,43(6):1485-1497.
[197]Zi-Jian Yang,Setsuo sagara and Teruo Tsuji.System Impulse Response Identification Using a Multiresolution Neural Network[J].Automatica,1997,33(7):1345-1350.
[198]张敏贵.基于小波和支持向量机的人脸识别方法研究[D].西北工业大学博士学位论文,2003.
[199]Zhang L,Zhou W D,Jiao L C.Wavelet Support Vector Machine[J].IEEE Trnas.Systems,Man,and Cybernetics-Part B:Cybernetics,2004,34(1):34-39.
[200]李元诚,李波,方廷健.基于小波支持向量机的非线性组合预测方法研究[J].信息与控制,2004,33(3):303-306.
[201]张莉,周伟达,焦李成.尺度核函数支撑矢量机[J].电子学报,2002,4:527-529.
[202]胡丹,肖建,车畅.尺度核支持向量机及在动态系统辨识中的应用[J].西南交通大学学报,2006,41(4):460-465.
[203]Daubenehies I.The Wavelet Transform,Time-frequency Localization and Signal Analysis[J].IEEE Trans.On Information Theory,1990,36(5):961-1005.
[204]Daubechies I.Ten Lectures on Wavelets[M].philadephia:the Society for Industrial and Applied Mathematics,1992.
[205]崔锦泰著,程正兴译.小波分析导论[M].西安交通大学出版社,1997.
[206]李建平.小波分析与信号处理--理论、应用及软件实现[M].重庆:重庆出版社,1997.
[207]C J C Burges.Geometry and invariance in kernel based methods[A].in Advance in Kernel Methods-Support Vector Learning[C].Cambridge,MA:MIT Press,1999,89-116.
[208]Scholkopf A B,Bugres C J C,Smola A J.Advances in Kernel Methods Support Vector Learning[M].MIT Press,1999.
[209]Stein E M.Topics in Harmonic Analysis Related to the Littlewood-Paley Theory [M].Princeton,New Jersey:Princeton University Press and the University of Tokyo Press,1970.
[210]李宁,尹森菁.边坡安全监测的仿真反分析[J].岩石力学与工程学报,1996,15(1):9-18.
[211]李宁,辛有良,韩炬,G.Swoboda.华盛顿地铁福特-图特站的仿真反分析[J].西安理工大学学报,1996,12(4):324-329.
[212]朱合华,杨林德,桥本正.深基坑工程动态施工反演分析与变形预报[J].岩土工程学报,1998,20(4):30-35.
[213]朱合华,丁文其.地下结构施工过程的动态仿真模拟分析[J].岩石力学与工程学报,1999,18(5):497-502.
[214]杨志法,熊顺成,王存玉,等.关于位移反分析的某些考虑[J].岩石力学与工程学报,1995,14(1):11-16.
[215]方开泰,马长兴.正交与均匀试验设计[M].北京:科学出版社,2001.
[216]赵同彬,谭云亮,张玉明,等.巷道工程位移反分析的可反演性评价研究[J].采矿与安全工程学报,2006,23(2):224-228.
[217]丁德馨,杨仕教,孙钧.岩体弹塑性模型力学参数对位移的影响度研究[J].岩石力学与工程学报,2003,22(5):697-701.
[218]邓聚龙.灰色预测与决策[M].武汉:华中理工大学出版社,1986:103-108.
[2]Kirsten H A D.Determination of rock mass elastic moduli by back analysis of deformation measurement[A].In:Proc Stmp on Expliration for Rock Eng[C].Johannesburg,1976,1154-1160.
[3]Maiar G,Jurina L,Podolak K.On model identification problem in rock mechanics [A].In:Proceedings symposium on the Geotechnics of Structurally Complex Formations[C].Capri,1977:257-261.
[4]Kovari K.Integrated Measuring Technique for Rock Pressure Determination[C].Int.Symp.On Measurement in Rock Mech.,Zurich,April,1977.
[5]Gioda G,Maier G.Direct search solution of an inverse problem in elasto-plasticity,indentification of cohesion,fricition angle and in-situ stress by pressure tunnel tests[J].Int.J.Num Methods in Eng,1980(15):1823-1834.
[6]Sakurai S,Takeuchi K.Back Analysis of measured displacement of tunnel[J].Rock Mech And Rock Eng,1983,16(3):173-180.
[7]杨林德.岩土工程问题的反演理论与工程实践[M].北京:科学出版社,1995:23-29.
[8]杨志法,王思敬,冯紫良,等.岩土工程反分析原理及应用[M].北京:地震出版社,2002:1-3.
[9]Pierpaolo Oreste.Back-analysis techniques for the improvement of the understanding of rock in underground constructions[J].Tunnelling and Underground Space Technology,2005(20):7-21.
[10]Sakurai S.Determination of initial stresses and mechanical Properties of viscoelastic underground medium[C].Proc.3~(rd) ISRM Cong.,Denver,1974,Π-B,1169-1174.
[11]刘允芳.弹性介质岩体中非圆形洞室位移反分析计算[J].岩石力学与工程学报,1986,5(5):141-144.
[12]薛琳,杨志法.粘弹性岩体力学参数的解析法[R].中科院地质研究所工程地质力学开放实验室1992年报.北京:地震出版社,1992:71-84.
[13]薛琳,杨志法.隧道周围粘弹性岩土介质蠕变柔量反演[R].中科院地质研究所工程地质力学开放实验室1992年报.北京:地震出版社,1992:178-190.
[14]Gioda G,Jurina L.Numerical identification of soil-structure interaction Pressures.Int.J.for Num.Anal.& Method in Geomech.,1981,(5):33-56.
[15]Wang Zhiyin,Liu Huaiheng.Back analysis of measured rheologic displacements of underground opening[C].In:Proe.6~(th) Conf.on Num.Meth.in Geomechanics,Austria,1988:2291-2297.
[16]杨林德.确定矿山巷道初始地应力方法的研究[J].同济大学学报,1986,14(2):161-166.
[17]杨志发,刘竹华.位移反分析在地下工程设计中的初步应用[J].地下工程,1981(2):20-24.
[18]杨志法,丁恩保,张三旗.地下工程平面问题弹性有限元图谱[M].北京:科学出版社,1989.
[19]吕爱钟,蒋斌松.岩石力学反问题[M].北京:煤炭工业出版社,1998.
[20]蒋斌松.巷道支架荷载反算方法[C].第四届全国岩土力学数值分析与解析方法讨论会论文集.武汉:武汉测绘科技大学出版社,1991,139-147.
[21]朱珍德,胡定.隧洞围岩压力位移反分析原理和方法[J].地下空间,1999,19(3):169-173.
[22]吕爱钟,蒋斌松.岩石力学反问题的几个基本问题[J].岩石力学与工程学报,2002,21(增刊):1921-1926.
[23]张中生,陈子萌,蒋斌松.地下结构荷载反算中解的稳定性研究[J].中国矿业,1999,8(5):79-84.
[24]张中生,陈子萌,朱维申.地下结构荷载的广义反演方法[J].土木工程学报,2001,34(2):38-42.
[25]张中生.地下结构荷载反算中的测线网优化布置[J].岩石力学与工程学报,2000,19(2):219-224.
[26]Gioda G.,etc.Back analysis procedures for the interpretation of field measurements in geomechanics[J].Int.J.for Num.& Anal.Methods in Geom.,1987(10):521-552.
[27]冯紫良,杨林德,李成江.初始地应力的反推原理[J].隧道工程,1985(4):44-50.
[28]冯紫良,杨林德.初始地应力的反推原理[J].同济大学学报,1983(3):18-25.
[29]杨林德,等.初始地应力位移反分析的有限单元法[J].同济大学学报,1985,(4):15-20.
[30]王芝银,刘怀恒.粘弹塑性有限元分析及其在岩石力学与工程中的应用[J].西安矿业学院学报,1985,5(1):86-101.
[31]陶振宇,曾庆义.地应力场的函数反分析[J].武汉水利电力学院学报,1987(3):21-27.
[32]庞作会,陈文胜,等.复杂初始地应力场的反分析[J].岩土工程学报,1998, 20(4):362-367.
[33]李守巨,张军,刘迎曦,等.基于优化算法的岩体初始应力场随机识别方法[J].岩石力学与工程学报,2004,23(23):4012-4016.
[34]易达,陈胜宏,葛修润.岩体初始应力场的遗传算法与有限元联合反演法[J]。岩土力学,2004,25(7):1077-1080.
[35]Arai R.An inverse problem approach to the prediction of Multi-dimensional consolidation behavior[J].Solids and Foundations,1984,24(1):95-108.
[36]朱志伟,冯紫良,刘学山.深基坑工程土层参数反演及挡墙内力预报[J].岩土力学,1999,20(4):63-68.
[37]刘学增,朱合华.考虑动态施工过程的岩土介质横观各向同性粘弹性反分析及其工程应用[J].岩土力学与工程学报,2002(1):89-92.
[38]刘迎曦,王登刚,李守巨,等.识别混凝土重力坝弹性模量的一种新方法[J].大连理工大学学报,2000,40(2):144-147.
[39]王复明,魏翠玲,周晶.路面结构的动态反分析[J].工程力学,2002,19(1):121-124,93.
[40]李宁,段小强,陈方方,等.围岩松动圈的弹塑性位移反分析方法探索[J].岩石力学与工程学报,2006,25(7):1304-1308.
[41]刘保国,郭忠平.岩体粘塑性流动系数γ的反演计算[J].岩土工程学报,1999,21(2):213-216.
[42]Gioda G,Sakurai S.Back analysis procedures for the interpretation of field measurements in geomechanics[J].Int.J.for Num.& Anal.Meth.in Geomech.,1987,11:555-583.
[43]袁勇,孙钧.岩体本构模型反演识别理论及其工程应用[J].岩石力学与工程学报,1993,12(3):232-39.
[44]袁勇,孙钧.岩土工程的系统辨识理论及工程应用[D].上海:同济大学,1991.
[45]高玮,郑颖人.基于遗传算法的岩土本构模型辨识[J].岩石力学与工程学报,2002,21(1):8-11.
[46]高玮,郑颖人.采用快速遗传算法进行岩土工程反分析[J].岩土工程学报,2001,23(1):120-122.
[47]高玮,郑颖人,冯夏庭.岩土本构模型识别的仿生算法研究[J].岩土力学,2004,25(1):31-36.
[48]高玮,郑颖人.基于生态竞争模型的岩土本构模型辨识新算法[J].岩土工程学报,24(1):93-97.
[49]高玮,冯夏庭.岩体本构模型智能识别的若干研究[J].岩石力学与工程学报, 2002,21(增2):2532-2538.
[50]刘保国,孙钧.岩体流变本构模型的辨识及其应用[J].北方交通大学学报,1998,22(4):10-14.
[51]孙钧.岩土材料流变及其工程应用[M].北京:中国建筑工业出版社,1999.
[52]朱珍德,徐卫亚.岩体粘弹性本构模型辨识及其工程应用[J].岩石力学与工程学报,2002,21(11):1605-1609.
[53]徐日庆,龚晓南,王明洋,等.枯弹性本构模型的识别与变形预报[J].水利学报,1998,(4):82-86.
[54]刘保国,孙钧.岩体粘弹性模型本构模型辨识的一种方法[J].工程力学,1999,16(1):12-17.
[55]刘世君,徐卫亚,邵建富.岩石粘弹性模型辨识及参数反演[J].水利学报,2002,(6):101-106.
[56]孙钧,蒋树屏,袁勇,等编著.岩石力学反演问题的随机理论与方法[M].汕头:汕头大学出版社,1996.
[57]黄宏伟,孙钧.基于Bayesian广义参数反分析[J].岩石力学与工程学报,1994,13(3):219-228.
[58]袁勇,孙钧.岩土工程优化反演的目标函数[J].岩石力学与工程学报,1994,13(2):29-37.
[59]朱永全,景诗庭,张清.围岩参数Monte-Carlo有限元反分析[J].岩土力学,1995,16(3):29-34.
[60]林育梁,樱井春铺.应用模糊有限元法的一种反分析形式[J].岩土工程学报,1995,17(5):48-52.
[61]蒋树屏.扩张卡尔曼滤波器有限元耦合算法及其隧道工程应用[J].土工程学报,1996,18(4):11-19.
[62]杨成祥,冯夏庭,陈炳瑞.基于扩展卡尔曼滤波的岩石流变模型参数辨识[J].岩石力学与工程学报,2007,26(4):754-761.
[63]陈斌.岩土工程随机反演分析及工程应用[D].河海大学博士论文,2001.
[64]陈斌,刘宁,周家守,等.岩土工程反分析的最大熵原理[J].河海大学学报(自然科学版),2002,30(6):52-55.
[65]Gioda G,Pnadolfi A,Cividini A.A comparative evaluation of some back analysis algorithms and their application to in-situ load tests[C].In:Proc.2~(nd) Int.Symp.on Field Measurement in Geom.,1987,1134-1144.
[66]吕爱钟.地下巷道弹性位移反分析各种优化方法的探讨[J].岩土力学,1996,17(2):29-34.
[67]孙钧,黄伟.岩石力学参数弹塑性反演问题的优化方法[J].岩石力学与工程学报,1992,11(3):221-229.
[68]席裕庚,柴天佑,恽为民.遗传算法综述[J].控制理论与应用,1996,13(6):697-708.
[69]陈建安,郭大伟,徐乃平,等.遗传算法理论研究综述[J].西安电子科技大学学报,1998,25(3):363-368.
[70]王登刚,刘迎曦,李守巨.岩土工程位移反分析的遗传算法[J].岩石力学与工程学报,2000,19(增刊):979-982.
[71]李守巨.基于计算智能的岩土力学模型参数反演方法及其工程应用[D].大连理工大学博士学位论文,2004.
[72]丁德馨,张志军,孙钧.弹塑性位移反分析的遗传算法研究[J].工程力学,2003,20(6):1-5.
[73]Colorni A,Dorigo M,Maniezzo V.Distributed Optimization by ant colonies[C].In:Varela F,Bougrine Ped.Proc 1st European Conefrence on Artifieial Life.France:Elsevier,1991,131-142.
[74]Dorigo M,Mnaiezzo V,Colorni A.The ant system:optimization by a colony of cooperating agents[J].IEEE Trans Syst Man Cybern-Part B,1996,26(1):29-41.
[75]Conre D,Dorigo M,Glover F.New ideas in optimization[M].London:Mc Grwa-Hill,1999.
[76]田明俊.智能反演算法及其应用研究[D].大连理工大学博士学位论文,2006.
[77]田明俊,周晶.基于蚁群算法的土石坝土体参数反演[J].岩石力学与工程学报,2005,24(8):1411-1416.
[78]Kennedy J,Eberhart R C.Particle swarm optimization[A].Proceedings of IEEE International Conference on Neural Network[C].New York:1995,1942-1948.
[79]Eberhart R C,Yuhui Shi.Particle swarm optimization:development,application and resources[A].Procedings of Evolutionary Computation[C].New York:IEEE Press.2001,81-86.
[80]高玮.基于粒子群优化的岩土工程反分析研究[J].岩土力学,2006,27(5):795-798.
[81]苏国韶,冯夏庭.基于粒子群算法的高地应力条件下硬岩本构模型的参数辨识[J].岩石力学与工程学报,2006,24(17):3030-3034.
[82]高玮,冯夏庭.基于免疫连续蚁群算法的岩土工程反分析研究[J].岩土力学与工程学报,2005,24(23):4266-4271.
[83]田明俊,周晶.岩土工程参数反演的一种新方法[J].岩石力学与工程学报, 2005,24(9):1492-1496.
[84]李守巨,刘迎曦,陈昌林,等.基于混合遗传算法的混凝土大坝力学参数反演[J].大连理工大学学报,2004,44(2):195-199.
[85]乐金朝,刘凤娥,王复明.路面结构模量反算的遗传—模拟退火算法[J].计算力学学报,2004,21(1):88-92.
[86]刘福深,刘耀儒,杨强,等.基于改进遗传算法的拱坝位移反分析[J].岩石力学与工程学报,2005,24(23):4341-4345.
[87]Feng Xia-Ting,Chen Bing-Rui,Yang Chengxiang,et al.Identification of visco-elastic models for rocks using genetic programming coupled with the modified particle swarm optimization algorithm[J].International Journal of Rock Mechanics and Mining Sciences,2006,43(5):789-801.
[88]Xia-ting Feng,Katsuyama K,Yong-jia Wang,et al.A new direction-intelligent rock mechanics and rock engineering[J].Int.J.rock Mechanics and Mining Science,1997.
[89]Feng Xia-Ting,Zhao Hongbo,Li Shaojun.A new displacement back analysis to identify mechanical geo-material parameters based on hybrid intelligent methodology [J].International Journal for Numerical and Analytical Methods in Geomechanics,2004,28(11):1141-1165.
[90]Shihui Li,Jie Yang,Weidong Hao,Yanjun Shang.Intelligent back-analysis of displacements monitored in tunneling[J].International Journal of Rock Mechanics &Mining Sciences,2006,(43):1118-1127.
[91]冯夏庭,张治强,杨成祥,等.位移反分析的进化神经网络方法研究[J].岩石力学与工程学报,1999,18(5):497-502.
[92]冯夏庭.智能岩石力学导论[M].北京:科学出版社,2000.
[93]张志军,丁德馨.位移反分析的人工神经网络方法研究[J].南华大学学报(自然科学版),2005,19(2):1-5.
[94]江权,冯夏庭,苏国韶,等.基于松动圈-位移增量监测信息的高地应力下洞室群岩体力学参数的智能反分析[J].岩石力学与工程学报,2007,26(增1):2654-2612.
[95]梁桂兰,徐卫亚,韦杰,等.位移反分析的APSO-WNN模型研究及应用[J].岩石力学与工程学报,2007,26(6):1251-1257.
[96]冯建龙,张孟喜.BP网络在双连拱隧道围岩参数反分析中的应用[J].上海大学学报(自然科学版),2005,11(3):293-298.
[97]易小明,陈卫忠,李术才,等.BP神经网络在分岔隧道位移反分析中的应用[J]. 岩石力学与工程学报,2006,25(增2):3927-3932.
[98]VAPNIK V.Statistical Learning Theory[M].New York:Wiley,1998.
[99]赵洪波.非线性岩土力学行为的支持向量机研究[M].中科院武汉岩土力学研究所,博士学位论文,2003.
[100]赵洪波,冯夏庭.位移反分析的进化支持向量机研究[J].岩石力学与工程学报,2003,22(10):1618-1622.
[101]许传华,任青文,周庆华.基于支持向量机和模拟退火算法的位移反分析[J].岩石力学与工程学报,2005,24(22):4134-4138.
[102]许传华,任青文,郑治,等.索风营水电站洞室岩体力学参数的位移反分析[J].岩土工程学报,2006,28(11):1981-1985.
[103]姜谙男.基于三维数值模拟-SVM非线性模型的大型洞室群围岩参数进化识别[J].水力发电学报,2006,25(5):97-101.
[104]刘开云,乔春生,刘保国.基于改进GA-SVR算法的隧道工程三维弹塑性模型参数的智能辨识[J].岩石力学与工程学报,2007,26(6):1164-1172.
[105]余志雄,周创兵,陈益锋,等.基于v-SVR和GA的初始地应力场位移反分析方法研究[J].岩土力学,2007,28(1):152-158.
[106]赵洪波.基于微粒群优化的智能位移反分析研究[J].岩土工程学报,2006,28(11):2035-2038.
[107]K.J.Bathe and E.L.Wilson.Numerical Method in Finite Element Analysis[M],1976.
[108]Belytschko T,Lu Y Y,Gu L.Element-free Galerkin method[J].Int.J.Num.Meth.Eng,1994,37(2):229-256.
[109]宋康祖,陆明万,张雄.固体力学中的无网格方法[J].力学进展,2000,30(3):55-56.
[110]Braun J,Sambridge M.A numerical method for solving partial differential equations on highly irregular evolving grids[J].Nature,1995,376:655-660.
[111]蔡永昌,朱合华.岩土工程数值计算中的无网格法及其全自动布点技术[J].岩土力学,2003,24(1):21-24.
[112]蔡永昌,朱合华,夏才初.无网格自然邻接点法及其在岩土工程数值模拟中的应用[J1.岩石力学与工程学报,2005,24(11):1888-1924.
[113]朱合华,杨宝红,蔡永昌,徐斌.无网格自然单元法在弹塑性分析中的应用[J].岩土力学,2004,25(4):671-674.
[114]张英新,王建华,高绍武.二维弹塑性自然单元法算法实现[J].上海交通大学学报,2005,39(5):727-730.
[115]Sukumar N,Moran,Belytschko T.The nature element method in solid mechanics[J].Int J Num Meth Eng,1998,43:839-887.
[116]N.Sukumar,B.Moran,A.Yu Semenov,et al.Natural neighbor Galerkin method[J].Int.J.Numer.Meth.Engng.,2001,50:1-27.
[117]Belikov V V,Semenov A Y.Non-Sibson interpolation on arbitrary system of points in Euclidean space and adaptive isolines generation[J].Applied Numerical Mathematics,2000,32:371-387.
[118]卢波,葛修润,王水林.自然单元法数值积分方案研究[J].岩石力学与工程学报,2005,24(1):1917-1924.
[119]Jeong Wahn Yoo,Brian Moran,Jiun-Shyan Chen.Stabilized conforming nodal integration in the natural-element method[J].Int.J.Numer.Meth.Engng.,2004,60:861-890.
[120]Bettess P,Zienkiewicz O C.Diffraction and refraction of surface waves using finite and infinite elements[J].International Journal for Numerical Methods in Engineering,1977,11:1271-1290.
[121]Astley R J,Eversman W.Wave envelope and infinite element schemes for fan noise radiation from turbofan inlets[C].AIAA-83-0709,1983.
[122]Astley R J,Macaulay G J.Mapped wave envelope elements for acoustical radiation and scattering[J].Journal of Sound and Vibration,1994,170(1):97-118.
[123]杨瑞梁,汪鸿振.一种新的声无限元法[J].振动与冲击,2003,22(3):21-24.
[124]赵崇斌,张楚汉,张光斗.用无穷元模拟半无限平面弹性地基[J].清华大学学报,1986,26(1):51-64.
[125]燕柳斌.用三维映射无限元模拟重力坝地基[J].水利学报,1991,10:7-12.
[126]周世良,胡晓,王江.无限元在岩土工程数值分析中的应用[J].重庆交通学院学报,2004,23(增刊):61-64.
[127]卢波.自然单元法的发展及其应用[D].中国科学院:武汉岩土力学所,博士学位论文,2005.
[128]张雄,刘岩.无网格法[M].北京:清华大学出版社,2004.
[129]孙钧.岩土材料流变及其工程应用[M].北京:中国建筑工业出版社,1999.
[130]孙钧,汪炳鉴.地下工程有限元解析[M].上海:同济大学出版社,1988.
[131]D.R.J.Owen,E.Hinton.Finite Element In Plasticity-Theory And Practice[M].Pinerige Press Limited,1980.
[132]李军强,刘宏昭,王忠民.线性粘弹性本构方程及其动力学应用研究综述[J].振动与冲击,2005,24(2):116-121.
[133]杨挺青.粘弹性力学[M].武汉:华中理工大学出版社,1990.
[134]Vapnik V.The nature of statistical learning theory[M].New York:Springer-Verlag,1999.
[135]张学工,译.统计学习理论的本质[M].北京:清华大学出版社,2000.
[136](英)克里斯特安尼(Cristianini,N.)等著:李国正,王猛,曾华军,译.支持向量机导论[M].北京:电子工业出版社,2004.
[137]邓乃扬,田英杰.数据挖掘中的新方法-支持向量机.北京:科学出版社,2004.
[138]张学工.关于统计学习理论与支持向量机[J].自动化学报,2000,26(1):37-42
[139]Cortes C.,Vapnik V.Support Vector Networks[J].Machine Learning,1995,Vol.20:273-297.
[140]Osuna E.,Freund R.An Improved Training Algorithm for Support Veetor Machines[C].In:Proceedings of the IEEE Workshop on Neural Networks for Signal Processing,1997.
[141]Platt J.C.Sequential Minimal Optimization:A Fast Algorithm for Training Support Vector Machines[R].Technical Report MSR-TR-98-14,Aprail,21,1998.
[142]Alex J Smola,Bernhard Schoelkopf.A tutorial on support vector regression[R].NeuroCOLT2 Technical Report Series NC2-TR-1998030,1998.
[143]Smola A,Murata N,Scholkopf B,Muller K.Asymptotically optimal choice of ε-loss for support vector machines[C].Proceedings of ICANN 1998.
[144]Kwok J T.Linear dependency between ε and the input noise in ε-support vector regression[A].In G.Dorffiner,H.Bishof,and K.Hornik(Eds.),ICANN2001,405-410.
[145]Mattera D,Haykin S.Support vector machines for dynamic reconstruction of a chaotic system[A].In B.Scholkopf,J.Burges,and A.Smola(Eds.),Advances in kernel methods:Support vector machine[M].Cambridge,MA:MIT Press,1999.
[146]Cherkassky V,Yunqian Ma.Practical Selection of SVM Parameters and Noise Estimation for SVM Regression[J].Neural Networks,2004,17:113-126.
[147]B.Baesens,S.Viaene,T.Van Gestel,J.A.K.Suykens,G..Dedene,B.De Moor,J.Vanthienen.An empirical assessment of kernel type performance for least squares support vector machine classification[C].Proceedings of Forth International on Knowledge-based Intelligent Engineer system and Allied Technologies.Brighton,UK 2000:313-316.
[148]K.Ito,R.Nakano.Optimizing Support Vector regression hyperparameters based on cross-validation[C].Proceedings of the International Joint Conference on Neural Networks.2003,3:2077-2082.
[149]Gavin C.,Cawley,Nicola L.C.,Talbot.Fast exact leave-one-out cross-validation of sparse least-squares support vector machines[J].Neural Networks.2004,17(10):1467-1475.
[150]郭辉,刘贺平,王玲.最小二乘支持向量机参数选择方法及其应用研究[J].系统仿真学报,2006,18(7):2033-2036,2051.
[151]Chapelle O.,Vapnic V.Choosing multiple parameters for support vector machines[J].Machine Learning,2002,(46):131-159.
[152]CHEN Pengwei,WANG Jungying,LEE Hahnming.Model selection of SVMs using GA approach[C].//Proc of 2004 IEEE Int Joint Conf on Neural Networks.Piscataway,NJ:IEEE Press,2004:2035-2040.
[153]ZHENG Chunhong,JIAO Licheng.Automatic parameters selection for SVM based on GA[C].//Proc of the 5th World Congress on Intelligent Control and Automation.Piscataway,NJ:IEEE Press,2004:1869-1872.
[154]杜京义,候媛彬.基于遗传算法的支持向量回归机参数选取[J].系统工程与电子技术,2006,28(9):1430-1433.
[155]陈果.基于遗传算法的支持向量机分类器模型参数优化[J].机械科学与技术,2007,26(3):347-350.
[156]邵信光,杨慧中,陈刚.基于粒子群算法的支持向量机参数选择及其应用[J].控制理论与应用,2006,23(5):740-744.
[157]李爱国.多粒子群协同优化算法[J].复旦学报(自然科学版),2004,43(5):923-925.
[158]吕振肃,侯志荣.自适应变异的粒子群优化算法[J].电子学报,2004,3:417-421
[159]Angeline P.Using selection to improve Particle swarm optimization[C].IEEE International Conference on Evolutionary Computation,Anchorage,Alaska,1998:84-89.
[160]Shi Y,Eberhart R.A modified Particle swarm optimizer[C].IEEE World Congress on Computational Intelligence,1998:69-73.
[161]刘建华,樊晓平,瞿志华.一种惯性权重动态调整的新型粒子群算法[J].计算机工程与应用,2007,43(7):68-70.
[162]郭文忠,陈国龙.粒子群优化算法中惯性权值调整的一种新策略[J].计算机工程与科学,2007,29(1):70-72,75.
[163]Clerc M.The swarm and the queen:towards a deterministic and adaptive particle swarm optimization[C].Proceedings of the 1999 Congress on Evolutionary computation,1999,.3:1951-1957.
[164]Kennedy J.Small worlds and mega-minds:effects of neighbourhood topology on particle swarm performance[C].Proceedings of IEEE Congress on Evolutionary Computation.1999,Vol.3:1931-1938.
[165]Higashi N,Iba H.Particle swarm optimization with Gaussian Mutation[C].//Proceedings of the 2003 Congress on Evolutionary Computation.Piscataway,NJ:IEEE Press,2003:72-89.
[166]高鹰,谢胜利.免疫粒子群优化算法[J].计算机工程与应用,2004,40(6):4-6.
[167]Brskar S,Suganthan P N.A Novel Concurrent Particle Swarm Optimization[C].//Proceedings of the 2004 Congress on Evolutionary Computation.Piscataway,NJ:IEEE Press,2004,792-796.
[168]Ven den Bergh F,Engelbrecht A.P..Using neighbourhoods with the guaranteed convergence PSO[C].Proceedings of the 2003 IEEE,Swarm Intelligence Symposium,2003:235-242.
[169]谭皓,沈春林,李锦.混合粒子群算法在高维复杂函数寻优中的应用[J].系统工程与电子技术,2005,27(8):1471-1474.
[170]陈贵敏,贾建援,韩琪.粒子群优化算法的惯性权值递减策略研究[J].西安交通大学学报,2006,(1):
[171]高鹰,谢胜利.基于模拟退火的粒子群优化算法[J].计算机工程与应用,2004,24(1):47-50.
[172]袁亚湘,孙文瑜,著.最优化理论与方法[M].北京:科学出版社,1997.
[173]G.Cauwenberghs,T.Poggio.Incremental and decremental support vector machine learning[C],in Advances in Neural Information Processing Systems,Cambridge,MA:MIT Press,2001,13:426-433.
[174]F.Perez-Cruz,A.Navia-Vazquez,R L.Alarcon-Diana,and A.Artes-Rodriguez.An IRWLS procedure for SVR[C].In Proc.of the EUSIPCO,Finland,Sept 2000.
[175]Suykens J A K,Vandewalle J.Least squares Support Vector Machines Classifiers[J].Neural Processing Letters,1999,9(3):293-300.
[176]J.A.K.Suykens,L.Lukas,et al.Sparse approximation using least squares support vector machines[C].In Proc.Of the IEEE International Symposium on Circuits and Systems(ISCAS 2000),Geneva,Switzerland,(2000):757-760.
[177]B J de Kruif,T J de Vries.Pruning error minimization in least squares support vector machines[J].IEEE Trans on Neural Networks,2003,14(3):696-702.
[178]X Y Zeng,X W Chen.SMO-based pruning methods for sparse least squares support vector machines[J].IEEE Trans on Neural Networks,2005,16(6):1541-1546.
[179]杨晓伟,路节,张广全.一种高效的最小二乘支持向量机分类器枝剪算法[J].计算机研究与发展,2007,44(7):1128-1136.
[180]甘志良,孙宗海,孙优贤.稀疏最小二乘支持向量机[J].浙江大学学报,2007,41(2):245-248.
[181]陶少辉,陈德钊,胡望明.最小二乘支持向量机分类器的高稀疏化及应用[J].系统工程与电子技术,2007,29(8):1351-1355.
[182]M.Espinoza,J.A.K.Suykens,B.D.Moor.Load forecasting using fixed-size least squares support vector machines[C].8th International Workshop on Artificial Neural Networks,IWANN 2005,Lecture Notes in Computer Science,2005,3512:1018-1026.
[183]M.Espinoza,J.A.K.Suykens,B.D.Moor.Fixed-size least squares support vector machines:a large scale application in electrical load forecasting[J].Computational Management Science,2006,(3):113-129.
[184]吴春国.广义染色体遗传算法与迭代式最小二乘支持向量机回归算法研究[D].吉林大学博士学位论文,2006.
[185]姜静清.最小二乘支持向量机算法及应用研究[D].吉林大学博士学位论文,2007.
[186]K.I.Diamantaras,S.Y.Kung.Principal Component Neural Networks:Theory and Applications[M].New York:John Wiley and Sons,1996.
[187]J.H.Liu,J.E Chen,et al.Online LS-SVM for function estimation and classification[J].Journal of University of Science and Technology,Beijing,2003,10(5):73-77.
[188]S.Vingaa,S.Jonas,J.A.Almeida.Renyi continuous entropy of DNA sequences [J].Journal of Theoretical Biology,2004,231:377-388.
[189]C.E.Shannon.A mathematical theory of communication[J].Bell Syst.Tech.J.1948,27:379-423,623-656.
[190]A.Renyi.On measures of entropy and information[C].Proceedings of the Fourth Berkeley Symposium on Mathematics,Statistics and Probability,University of California Press,Berkeley,CA,1961,1:547-561.
[191]A.Renyi.Introduction a la theorie de linformation.Calcul des probabilites[M]. Dunod,Paris,1966.
[192]M.Girolami.Orthogonal series density estimation and the kernel eigenvalue problem[J].Neural Computation,2002,14(3):669-688.
[193]刘贵忠,邸双亮.小波分析及其应用[M].西安:西安电子科技大学出版社,1992.
[194]Zhang Q H,Benveniste A.Wavelet network[J].IEEE Trans on Neural Network,1992,3(6):889-898.
[195]Zhang Q.Using Wavelet Networks in Nonparametric Estimation[J].IEEE Tmas.Neural Networks,1997,8(2):227-236.
[196]Zhang J,Walter G G.,Lee W N W.Wavelet Neural Networks for Function Learning[J].IEEE Trs.Signal Processing,1995,43(6):1485-1497.
[197]Zi-Jian Yang,Setsuo sagara and Teruo Tsuji.System Impulse Response Identification Using a Multiresolution Neural Network[J].Automatica,1997,33(7):1345-1350.
[198]张敏贵.基于小波和支持向量机的人脸识别方法研究[D].西北工业大学博士学位论文,2003.
[199]Zhang L,Zhou W D,Jiao L C.Wavelet Support Vector Machine[J].IEEE Trnas.Systems,Man,and Cybernetics-Part B:Cybernetics,2004,34(1):34-39.
[200]李元诚,李波,方廷健.基于小波支持向量机的非线性组合预测方法研究[J].信息与控制,2004,33(3):303-306.
[201]张莉,周伟达,焦李成.尺度核函数支撑矢量机[J].电子学报,2002,4:527-529.
[202]胡丹,肖建,车畅.尺度核支持向量机及在动态系统辨识中的应用[J].西南交通大学学报,2006,41(4):460-465.
[203]Daubenehies I.The Wavelet Transform,Time-frequency Localization and Signal Analysis[J].IEEE Trans.On Information Theory,1990,36(5):961-1005.
[204]Daubechies I.Ten Lectures on Wavelets[M].philadephia:the Society for Industrial and Applied Mathematics,1992.
[205]崔锦泰著,程正兴译.小波分析导论[M].西安交通大学出版社,1997.
[206]李建平.小波分析与信号处理--理论、应用及软件实现[M].重庆:重庆出版社,1997.
[207]C J C Burges.Geometry and invariance in kernel based methods[A].in Advance in Kernel Methods-Support Vector Learning[C].Cambridge,MA:MIT Press,1999,89-116.
[208]Scholkopf A B,Bugres C J C,Smola A J.Advances in Kernel Methods Support Vector Learning[M].MIT Press,1999.
[209]Stein E M.Topics in Harmonic Analysis Related to the Littlewood-Paley Theory [M].Princeton,New Jersey:Princeton University Press and the University of Tokyo Press,1970.
[210]李宁,尹森菁.边坡安全监测的仿真反分析[J].岩石力学与工程学报,1996,15(1):9-18.
[211]李宁,辛有良,韩炬,G.Swoboda.华盛顿地铁福特-图特站的仿真反分析[J].西安理工大学学报,1996,12(4):324-329.
[212]朱合华,杨林德,桥本正.深基坑工程动态施工反演分析与变形预报[J].岩土工程学报,1998,20(4):30-35.
[213]朱合华,丁文其.地下结构施工过程的动态仿真模拟分析[J].岩石力学与工程学报,1999,18(5):497-502.
[214]杨志法,熊顺成,王存玉,等.关于位移反分析的某些考虑[J].岩石力学与工程学报,1995,14(1):11-16.
[215]方开泰,马长兴.正交与均匀试验设计[M].北京:科学出版社,2001.
[216]赵同彬,谭云亮,张玉明,等.巷道工程位移反分析的可反演性评价研究[J].采矿与安全工程学报,2006,23(2):224-228.
[217]丁德馨,杨仕教,孙钧.岩体弹塑性模型力学参数对位移的影响度研究[J].岩石力学与工程学报,2003,22(5):697-701.
[218]邓聚龙.灰色预测与决策[M].武汉:华中理工大学出版社,1986:103-108.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |